Polynomial Graphing Calculator

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The highest power of x in your polynomial.
Coefficient of x^3. Set to 0 if not needed for your degree.
Coefficient of x^2.
Coefficient of x (the linear term).
The constant (y-intercept) term.
Polynomial
P(x) = x^3 - x

The polynomial as entered

Real rootsx = -1, x = 0, x = 1
y-intercept0
Critical pointsx = -0.5774, y = 0.3849 (max); x = 0.5774, y = -0.3849 (min)
Inflection pointsx = 0, y = 0
End behaviorFalls to -infinity as x -> -inf, rises to +infinity as x -> +inf
Derivative P'(x)P'(x) = 3x^2 - 1

P(x) = x^3 - x graphed

  • The polynomial has degree 3, so it can have at most 3 real roots and at most 2 turning points.
  • Found 3 real roots: x = -1, x = 0, x = 1.
  • Critical points (local extrema): x = -0.5774, y = 0.3849 (max); x = 0.5774, y = -0.3849 (min).
  • End behavior: Falls to -infinity as x -> -inf, rises to +infinity as x -> +inf.

Next stepTry adjusting coefficients to shift, stretch, or flip the curve. Setting a coefficient to 0 reduces the effective degree.

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